mirror of
https://github.com/c-sooyoung/fold_slice.git
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100 lines
3.9 KiB
Matlab
100 lines
3.9 KiB
Matlab
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% function fourier_interpolate(val,theta,numord)
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% This function uses a Fourier transform approximation to obtain the zero
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% and first coefficient of a periodic function (a sine wave fit) if only data
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% of half a period is available. Data within 0 and 180 degrees (inclusive)
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% is given. Completes and takes fft of data, theta is only used for some
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% checks, should be given in radians.
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%
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% a*sin(x*pi/180+b)+c
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% Output phase is in radians
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%
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% It is meant to work with equally spaced angles in the range of 180
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% degrees, including 180 degrees. It allows not exactly equally spaced but then
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% accuracy cannot be guaranteed.
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%
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% Optional parameter numord can be used in order to retrieve higher orders
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% of the fit
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%*-----------------------------------------------------------------------*
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%| |
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%| Except where otherwise noted, this work is licensed under a |
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%| Creative Commons Attribution-NonCommercial-ShareAlike 4.0 |
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%| International (CC BY-NC-SA 4.0) license. |
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%| |
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%| Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch) |
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%| |
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%| Author: CXS group, PSI |
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%*-----------------------------------------------------------------------*
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% You may use this code with the following provisions:
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%
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% If the code is fully or partially redistributed, or rewritten in another
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% computing language this notice should be included in the redistribution.
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%
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% If this code, or subfunctions or parts of it, is used for research in a
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% publication or if it is fully or partially rewritten for another
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% computing language the authors and institution should be acknowledged
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% in written form in the publication: “Data processing was carried out
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% using the “cSAXS matlab package” developed by the CXS group,
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% Paul Scherrer Institut, Switzerland.”
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% Variations on the latter text can be incorporated upon discussion with
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% the CXS group if needed to more specifically reflect the use of the package
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% for the published work.
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%
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% A publication that focuses on describing features, or parameters, that
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% are already existing in the code should be first discussed with the
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% authors.
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%
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% This code and subroutines are part of a continuous development, they
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% are provided “as they are” without guarantees or liability on part
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% of PSI or the authors. It is the user responsibility to ensure its
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% proper use and the correctness of the results.
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function fit = fourier_interpolate(val,theta,numord,sym_flip)
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% sym_flip For a function that is only measured from 0 to 180 then the
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% data is flipped mirrored in order to complete the period of
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% the sinewave
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% theta = [0:45:180]*pi/180;
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% val = 5 + sin(theta+0.5);
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if nargin<3
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numord = 1;
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end
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if ~exist('sym_flip')
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sym_flip = true;
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end
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% if any(theta)>1.05*pi;
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% error('This routine cannot account for angles larger than 180 at the moment')
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% end
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if ~all(size(theta)==size(val))
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error(['theta and val dont have the same number of elements'])
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end
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val = val(:);
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theta = theta(:);
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clear auxval
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if sym_flip
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auxval = [val(:);-fliplr(val(2:end-1))+val(1)+val(end)];
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else
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auxval = val;
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end
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auxfft = fft(auxval)/numel(auxval);
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fit.a = abs(auxfft(2:1+numord)*2*1i);
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fit.b = angle(auxfft(2:1+numord)*2*1i);
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fit.c = auxfft(1);
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% thetafine = linspace(0,pi,100);
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% figure(1);
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% plot(theta,val,'.-')
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% hold on
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% plot(thetafine,fit.a*sin(thetafine+fit.b)+fit.c,'-r')
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% hold off
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%
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% figure(2);
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% plot(auxval,'.-');
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